Symmetry-resolved entanglement of two-dimensional symmetry-protected topological states

Symmetry-resolved entanglement is a useful tool for characterizing symmetry-protected topological states. In two dimensions, their entanglement spectra are described by conformal field theories but the symmetry resolution is largely unexplored. However, addressing this problem numerically requires system sizes beyond the reach of exact diagonalization. Here, we develop tensor-network methods that can access much larger systems and determine universal and nonuniversal features in their entanglement. Specifically, we construct one-dimensional matrix product operators that encapsulate all the entanglement data of two-dimensional symmetry-protected topological states. We first demonstrate our approach for the Levin-Gu model. Next, we use the cohomology formalism to deform the phase away from the fine-tuned point and track the evolution of its entanglement features and their symmetry resolution. The entanglement spectra are always described by the same conformal field theory. However, the levels undergo a spectral flow in accordance with an insertion of a many-body Aharonov-Bohm flux.

Automated summary

Symmetry-resolved entanglement is a useful tool for characterizing symmetry-protected topological states. We developed tensor-network methods to study the entanglement data of two-dimensional symmetry-protected topological states by constructing matrix product operators. We verified our approach using the Levin-Gu model and tracked the evolution of entanglement features and their symmetry resolution by using the cohomology formalism.